Mathematics
Find two positive integers such that their product is 1,00,000 and none of them contains 0 as a digit.
Answer
1,00,000 = 105 = (2 × 5)5 = 25 × 55.
To ensure neither number contains 0 as a digit, we group all the 2's into one number and all the 5's into the other:
25 = 32
55 = 3125
Verification: 32 × 3125 = 1,00,000. ✓
Neither 32 nor 3125 contains 0 as a digit.
Hence, the two positive integers are 32 and 3125.
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